Eddie, Guitar Center has Baby Taylors for $369:

https://www.guitarcenter.com/search?typeAheadSuggestion=true&typeAheadRedirect=true&fromRecentHistory=false&Ntt=baby+taylors

But the body depth is 4":

https://www.taylorguitars.com/guitars/acoustic/features/shapes/big-baby

Yamaha has a JR2 3/4 size acoustic for $170 at Guitar Center but the body depth is 3.5".

ZZounds has an Ibanez thin body classical guitar with a 2.75" body depth for $300:

https://www.zzounds.com/item--IBAGA35TCE

Amazon has a number of thin body guitars that are in your price range:

https://www.amazon.com/s?k=thin+body+electric+acoustic+guitar&hvadid=77790500402761&hvbmt=be&hvdev=c&hvqmt=e&tag=mh0b-20&ref=pd_sl_887lbu6hi0_e

I hope this helps and good luck.

Whenever I get something stuck in the back of my throat, I dislodge it by drinking a beer.
It's called the Heineken Maneuver.

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software/hardware